Accelerometers measure acceleration, and gravitometers and gradiometers measure the acceleration of gravity, generally by measuring the displacement of a mass when it is acted upon by the acceleration. In the case of a classical accelerometer, the displacement of a proof mass suspended by a pair of springs is measured. This displacement is proportional to the acceleration and can be sensed and scaled to provide an indication of the magnitude of the acceleration. In the case of gravitometers, instruments have been constructed that measure the free fall time of a mass, the period of a pendulum, and small shifts in an excited quantum state. Ring laser gyroscopes have been used to measure angular acceleration, but optical means of measuring linear acceleration have not been practical.
For example, a Michelson-Morley (FIG. 1) or a Mach-Zender (FIG. 2) interferometer, in principle, could be used to measure acceleration. This follows from the fact that an acceleration changes the wavelength of light according to the principles of general relativity and optics.
Specifically, interferometers are designed to measure small optical path length changes. This is accomplished by splitting a light beam into two beams, sending each beam through a different path and then recombining the beams. If the beams encounter different optical path lengths they will arrive with slightly different delays. If the difference in optical paths is an even number of wavelengths of the light constructive interference occurs; if it is an odd number of wavelengths of the light destructive interference results. A continuum exists between these extremes, with constructive interference producing the strongest output signal and destructive interference the weakest (ideally none). Pictorially, one can imagine two sine waves being added as they slide past one another. When the positive peaks align the output is a sine wave of double amplitude, whereas when the positive peaks of the first sine wave aligns with negative peaks of the second sine wave the output goes to zero. Depending on the interferometer design, the interference pattern can produce a “bulls-eye” pattern or a series of dark and light bands due to differences in optical path length across the aperture of the interferometer.
Referring to FIG. 1, and assuming that the interferometer is accelerating from left to right, light traveling in arm 120 of the Michelson-Morley interferometer 100 will experience acceleration normal to the beam, while light traveling in arm 130 will experience acceleration along the beam. Relativistic effects will cause a minute wavelength shift between the two arms and in principle acceleration could be measured. However, the symmetry of the Michelson-Morley interferometer results in cancellation of first order acceleration effects, reducing the sensitivity of the device. That is, the beam traveling along arm 130 travels first in the direction of the acceleration, and then, after reflecting off of mirror 135, travels in the opposite direction in the arm, thereby canceling the first order acceleration effects.
Similarly, a Mach-Zender interferometer 200 (FIG. 2) can in principle measure acceleration gradients or gravitational field gradients. With this interferometer the light in arm 220 experiences a slightly different average gravitational field than the light in arm 230. This results in minuscule differences in wavelength between the two beams and thus an interference pattern at 240. This particular configuration has been used successfully to measure gravitational gradients using quantum interference between neutrons (as opposed to photons.) The neutrons have wavelengths (DeBrogle waves) that are many orders of magnitude shorter than light or even x-rays. This allows a measurable signal to be produced.
A problem with the Michelson-Morley and Mach-Zender interferometers is that for normally encountered gravitational fields, accelerations, and interferometer dimensions, the wavelength shifts and resulting interference shifts for optical interferometers are too small to measure using optical means.